Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,6,3,6}

Atlas Canonical Name {2,2,6,3,6}*864

Overview

Group
SmallGroup(864,4704)
Rank
6
Schläfli Type
{2,2,6,3,6}
Vertices, edges, …
2, 2, 6, 9, 9, 6
Order of s0s1s2s3s4s5
6
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

9-fold

Covers minimal covers in bold

2-fold

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := (14,23)(15,24)(16,25)(17,26)(18,27)(19,28)(20,29)(21,30)(22,31);;
s3 := ( 5,14)( 6,16)( 7,15)( 8,20)( 9,22)(10,21)(11,17)(12,19)(13,18)(24,25)(26,29)(27,31)(28,30);;
s4 := ( 5, 9)( 6, 8)( 7,10)(11,12)(14,27)(15,26)(16,28)(17,24)(18,23)(19,25)(20,30)(21,29)(22,31);;
s5 := ( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s3*s4*s3*s4*s3*s4, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, 
s5*s3*s4*s5*s4*s5*s3*s4*s5*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(31)!(1,2);
s1 := Sym(31)!(3,4);
s2 := Sym(31)!(14,23)(15,24)(16,25)(17,26)(18,27)(19,28)(20,29)(21,30)(22,31);
s3 := Sym(31)!( 5,14)( 6,16)( 7,15)( 8,20)( 9,22)(10,21)(11,17)(12,19)(13,18)(24,25)(26,29)(27,31)(28,30);
s4 := Sym(31)!( 5, 9)( 6, 8)( 7,10)(11,12)(14,27)(15,26)(16,28)(17,24)(18,23)(19,25)(20,30)(21,29)(22,31);
s5 := Sym(31)!( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31);
poly := sub<Sym(31)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s4*s3*s4*s3*s4, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, 
s5*s3*s4*s5*s4*s5*s3*s4*s5*s4 >;